In the Israeli Electrostatic Accelerator FEL, the distance between the accelerator's end and the wiggler's entrance is about 2.1 m, and 1.4 MeV electron beam is transported through this space using four similar quadrupoles (FODO-channel). The transfer matrix method (ABCD matrix method) was used for simulating the beam transport, a set of programs is written in the several programming languages (MATHEMATICA, MATLAB, MATCAD, MAPLE) and reasonable agreement is demonstrated between experimental results and simulations. Comparison of ABCD matrix method with the direct "numerical experiments" using EGUN, ELOP, and GPT programs with and without taking into account the space-charge effects showed the agreement to be good enough as well. Also the inverse problem of finding emittance of the electron beam at the S1 screen position (before FODO-channel), by using the spot image at S2 screen position (after FODO-channel) as function of quad currents, is considered. Spot and beam at both screens are described as tilted eellipses with diameters and orientation angle of which being found by STB (Spot-to-Beam) procedure, and trace-ellipse transformation is used to found emittance at S1 position.

We describe the interactive "STB" (spot_to_beam) MATHEMATICA procedure for a) approximating the spot image at the screen as ellipse, b) getting five parameters of the elliptic beam (two diameters, center coordinates, and orientation angle). The basic idea is to "map" the reference holes at screen onto the X-Y plane normal to the beam direction (Z-axis). All distortions of the image, e.g., due to camera-screen disposition can be, in principle, taken into account,assuming that the hole positions at screen and the orientation of the screen are known. With the non-linear LMS fitting, the "curved-coordinate-system" of the holes at image is transferred to the Cartesian coordinate system at XY-plane. Then the fitting ellipse is found in this latter system, by solving the system of N linear equations for 5 unknown parameters of beam ellipse, where N>5 is a number of reference points on edge of spot image. The examples of the real measurements at various screens will be demonstrated. The accuracy of beam diameters is about .1 mm depending on quality of picture and the perator's experience. The procedure is to be used in the routine measurements in the Israeli FEL.